Solve 3a^2-12a^3+7+8a

$$3 a ^ { 2 } - 12 a ^ { 3 } + 7 + 8 a$$

Differentiate w.r.t. a

$$8+6a-36a^{2}$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times 3a^{2-1}+3\left(-12\right)a^{3-1}+8a^{1-1}$$

Multiply 2 times 3.

$$6a^{2-1}+3\left(-12\right)a^{3-1}+8a^{1-1}$$

Subtract 1 from 2.

$$6a^{1}+3\left(-12\right)a^{3-1}+8a^{1-1}$$

Multiply 3 times -12.

$$6a^{1}-36a^{3-1}+8a^{1-1}$$

Subtract 1 from 3.

$$6a^{1}-36a^{2}+8a^{1-1}$$

Subtract 1 from 1.

$$6a^{1}-36a^{2}+8a^{0}$$

For any term t, t^{1}=t.

$$6a-36a^{2}+8a^{0}$$

For any term t except 0, t^{0}=1.

$$6a-36a^{2}+8\times 1$$

For any term t, t\times 1=t and 1t=t.

$$6a-36a^{2}+8$$

Evaluate

$$7+8a+3a^{2}-12a^{3}$$